Mark the correct statement (s) regarding friction .

Options

A. Friction force can be zero though the contact surface is rough
B. Even though there is no relative motion between surface friction force may exist between then
C. The expressions `f_(L) = mu_(s) N or f_(k) = mu_(s)N ` are approximate expressions
D. The expression `f_(L) = mu_(s)N ` rells that the direction of `f_(L)` and `N` are the same.

Explanation

To solve the question regarding the correct statements about friction, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Option A: Friction force can be 0 though the contact surface is rough.**
- **Analysis:** This statement is true. For example, if a block is resting on a rough surface but no external horizontal force is acting on it, the static friction force can be zero. Static friction can vary from 0 to a maximum value (μs * N), where N is the normal force. If there is no force trying to move the block, the friction force is zero.
- **Conclusion:** **Correct.**

2. **Option B: Even though there is no relative motion between the surfaces, friction force may exist between them.**
- **Analysis:** This statement is also true. For instance, if a horizontal force is applied to a block on a rough surface but is less than the maximum static friction (μs * N), the block will not move. In this case, the friction force will equal the applied force, thus existing even without relative motion.
- **Conclusion:** **Correct.**

3. **Option C: The expressions f_s = μ_s * N and f_k = μ_k * N are approximate expressions.**
- **Analysis:** This statement is true as well. The static friction force (f_s) can vary from 0 to μ_s * N, and kinetic friction (f_k) is often treated as a constant value (μ_k * N) but can vary based on conditions. Therefore, these expressions are approximations.
- **Conclusion:** **Correct.**

4. **Option D: The expression f_L = μ_s * N realizes that the direction of f_L and N are the same.**
- **Analysis:** This statement is incorrect. The normal force (N) acts perpendicular to the surface, while the friction force (f_L) acts parallel to the surface. Therefore, they are not in the same direction; in fact, they are at a 90-degree angle to each other.
- **Conclusion:** **Incorrect.**

### Final Answer:
The correct statements regarding friction are **A, B, and C**.

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